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摘要：迭代法是非线性方程求根最为常用的方法，常见的有简单迭代法，Steffensen迭代法，弦截法等。本文我们运用这几个迭代法进行组合优化，给出了两种新的迭代格式。
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第一种是将简单迭代法结合Steffensen迭代法，提出了一个新的迭代格式，并给出了matlab编程。用新的迭代格式求解非线性方程的根，与简单迭代法和steffensen迭代法相比，具有收敛速度快、迭代次数少等优点。22647
第二种是引入牛顿二次插值多项式，对弦截法进行改进，得到新的迭代格式用来求解非线性方程的根，与弦截法相比，具有迭代次数少等优点。
另外，我们将改进的简单迭代法由一文情况推广到二文，得到新的迭代格式，用来求解非线性方程组的解，与简单迭代法二文情况下相比，具有迭代次数少，误差小等优点。
毕业论文关键词：非线性方程 简单迭代法 Steffensen加速法 弦截法
Improvements on the Iterative Method for Non-linear Equation
Abstract:
The iterative method is the most commonly used in solving the nonlinear equations.For examples, simple iterative method, steffensen iteration method and secant method,etc. In the article, we apply the iterative method for combinatorial optimization and the two new iterative format is given.
Firstly, we combined simple iterative method with steffensen iteration method for suggesting a new iterative format and the matlab programming is given. With a new iterative format of solving nonlinear equation, it has the advantages of fast convergence speed and less number of iterations, compared with the simple iterative method and steffensen iteration method.
Secondly, the Newton quadratic interpolation polynomial is introduced to improve the secant method. With a new iterative format of solving nonlinear equation, it has the advantages of less number of iterations, compared with the secant method.
Moreover, we generalized the improved simple iterative method to two-dimensional by one-dimensional conditions. With a new iterative format of solving nonlinear equations, it has the advantages of less number of iterations and close rolerance, compared with the simple iterative method in the two-dimensional case.
Keywords: Nonlinear equation, Simple iterative method, Steffensen iteration method ,Secant method
目录
1 引言 5
1.1 课题的目的和意义 5
1.2 国内外研究现状与发展趋势 6
1.3 主要研究内容 6
2 非线性方程求解的迭代法介绍及应用举例 7
2.1 二分法 7
2.1.1 二分法的定义 7
2.1.2 误差估计 7
2.1.3 实例 7
2.2 简单迭代法 8
2.2.1 简单迭代法的定义 8
2.2.2 误差估计 9
2.2.3 实例 10
2.3 牛顿迭代法 10
2.3.1 牛顿迭代法的定义 10
2.3.2 误差估计 11
2.3.3 实例 11
2.4 弦截法 12
2.4.1 弦截法的定义 12
2.4.2 误差估计 13
2.4.3 实例 13
2.5 Steffensen迭代法 13
2.5.1 Steffensen迭代法的定义 13